Question: Simplify the following expression: $ a = \dfrac{5y - 5}{-4y + 9} + \dfrac{9}{2} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{2}{2}$ $ \dfrac{5y - 5}{-4y + 9} \times \dfrac{2}{2} = \dfrac{10y - 10}{-8y + 18} $ Multiply the second expression by $\dfrac{-4y + 9}{-4y + 9}$ $ \dfrac{9}{2} \times \dfrac{-4y + 9}{-4y + 9} = \dfrac{-36y + 81}{-8y + 18} $ Therefore $ a = \dfrac{10y - 10}{-8y + 18} + \dfrac{-36y + 81}{-8y + 18} $ Now the expressions have the same denominator we can simply add the numerators: $a = \dfrac{10y - 10 - 36y + 81}{-8y + 18} $ $a = \dfrac{-26y + 71}{-8y + 18}$ Simplify the expression by dividing the numerator and denominator by -1: $a = \dfrac{26y - 71}{8y - 18}$